lim cos2x/(sinx-cosx) x→π/4 求函数的极限

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lim cos2x/(sinx-cosx) x→π/4 求函数的极限
lim cos2x/(sinx-cosx) x→π/4 求函数的极限

lim cos2x/(sinx-cosx) x→π/4 求函数的极限
lim cos2x/(sinx-cosx)
=lim (cosx+sinx)(cosx-sinx)/(sinx-cosx)
=lim- (cosx+sinx)
=-√2

lim(x→π/4)cos2x/(sinx-cosx) 分子,分母都趋于0, 则可以用罗比达法则,分别对分子 ,分母求导
lim(x→π/4)cos2x/(sinx-cosx)
limx趋于π/4-2sin2x/(cosx+sinx )
= - 根号2